Add Digits - Digital Root

There's a mathematical property called the digital root. For any number $n > 0$, the digital root equals $1 + ((n - 1) \bmod 9)$.

Why does this work? A number and the sum of its digits have the same remainder when divided by $9$. Repeatedly summing digits preserves this remainder until you get a single digit.

Special case: if $n = 0$, the answer is $0$. Otherwise, use the formula. This gives you $O(1)$ time instead of $O(\log n)$.